JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech IV Year DIGITAL CONTROL SYSTEMS Previous Question Paper (July/August - 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
Solve the following:
With neat sketches, explain the principle of sample and hold circuit.
Answer
- A Sample and Hold (S/H) circuit is a fundamental component in digital control systems that bridges the gap between continuous-time (analog) signals and discrete-time (digital) processing.
- The circuit operates in two distinct modes: Sampling mode (tracking) and Hold mode.
- In Sampling mode, the switch is closed, allowing the output voltage to track the input analog signal. The capacitor charges or discharges to follow the input waveform.
- In Hold mode, the switch is opened. The capacitor maintains the voltage level it reached at the exact moment of switching, providing a constant output value for the duration of the sampling interval.
- This process effectively creates a staircase approximation of the original continuous signal, which is necessary for the A/D converter to sample a stable value without errors caused by signal fluctuations during the conversion time.
- Key components include a high-impedance buffer amplifier (to prevent capacitor discharge), a fast-acting electronic switch, and a high-quality holding capacitor.
Find ZOH equivalent transfer function of 10/(5s+1) obtained with the sampling period of Ts = 0.5 sec.
Answer
- The Zero-Order Hold (ZOH) equivalent transfer function, denoted as G(z), is given by the formula: G(z) = (1 - z^-1) * Z{G(s)/s}.
- Given G(s) = 10 / (5s + 1) and T = 0.5 sec, we first express G(s)/s using partial fraction expansion: G(s)/s = 10 / [s(5s + 1)] = 10 / [s(s + 0.2) * 5] = 2 / [s(s + 0.2)].
- Expanding into partial fractions: 2 / [s(s + 0.2)] = A/s + B/(s + 0.2). Solving for coefficients: A = 2/0.2 = 10; B = -10.
- So, G(s)/s = 10/s - 10/(s + 0.2).
- Taking the Z-transform: Z{G(s)/s} = 10 * [z / (z - 1)] - 10 * [z / (z - e^(-0.2 * 0.5))].
- Calculate the exponential term: e^(-0.1) ≈ 0.9048.
- Z{G(s)/s} = 10z / (z - 1) - 10z / (z - 0.9048).
- Now apply the ZOH formula: G(z) = (z - 1)/z * [10z / (z - 1) - 10z / (z - 0.9048)].
- G(z) = 10 - 10(z - 1) / (z - 0.9048) = [10(z - 0.9048) - 10(z - 1)] / (z - 0.9048).
- G(z) = [10z - 9.048 - 10z + 10] / (z - 0.9048) = 0.952 / (z - 0.9048).
What is sampling? Discuss various types of sampling operations.
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Solve the following:
Determine the z-transform of the following: i) ii) cos(4t)
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Obtain the relation between s-plane and z-plane.
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Solve the following:
State and explain Jury stability test.
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Obtain the closed loop pulse transfer function of the given system.
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Solve the following:
Determine the controllability of a discrete time control system given below: X(k+1) = AX(k) + Bu(k) and Y(k) = [1 0]X(k).
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Explain the controllability and observability applied to discrete time control systems. Can you say that duality exists between them?
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Solve the following:
State and explain Lyapunov stability applied in stability analysis of discrete time control systems.
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Investigate the controllability and observability of the provided system matrices.
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Consider the system X(k+1) = FX(k) + Gu(k) and y(k) = CX(k). Determine a suitable state feedback gain matrix K such that the system will have the closed loop poles at Z = (0.5 ± j0.3) and Z = 0.8.
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Explain the design procedure of Fast Output Sampling (FOS) and periodic output feedback controller for discrete time systems.
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